Splash Biography

"If you ever read about astrophysics, you hear about these huge flaming balls at distances of hundreds of light-years in which nuclear fusion of hydrogen into helium (or helium into carbon, or carbon into all kinds of stuff...) produces massive quantities of energy. Scientists talk about the ""diameter"" of stars. The color of stars. The temperature of stars. The age of stars. But... you look up, and stars are just these tiny dots in the sky. We don't have any telescopes powerful enough to enlarge them to anything *other* than tiny dots in the sky. How in the world can we figure so much out about stars if we can barely see them? Find out in this lightning tour of our galaxy."

"Addition and multiplication seem like such basic ideas. You can add numbers, and you can multiply numbers, and that's all there is. But what if you could add or multiply things that *aren't* numbers? This fundamental mathematical generalization opens up a new world of much richer ideas, and uncovers the truth about algebra. We're going to study ring theory, one branch of algebra that investigates what happens with a set in which you can add and multiply. We'll focus on polynomial rings while developing ring theory in general. This class is going to be extremely fast and abstract, so be prepared for quite a ride if you come! You should be familiar with high school algebra in full and ideally know polynomial division."

Do you get the sense that you should enjoy doing math but the problems you do in school are always boring, repetitive, and rote? There are thousands of deep, fun, *interesting* math problems, and this class will be an exploration of some of my favorites. Problems will range from basic problems that everyone can approach to olympiad-level problems. You'll be able to work on your own, teaming up with others in the class to work on the problems you get stuck on."